Thanks to Spurs' 2-1 win over Chelsea and their own last-gasp win over Manchester City last week, United are now one point behind Carlo Ancelotti's team, who host Stoke City on Sunday.
With games against Spurs, Sunderland and Stoke to come United could finish with a flourish, pouring the pressure on a Chelsea side who still have to visit Liverpool before finishing off against Wigan Athletic, who beat the Londoners at home in September.
With three weekends of action remaining the race for the Premier League title remains one of the closest and most exciting for years, though Arsenal, now six points off the pace after their defeat at Wigan, look out of the running even if they beat Manchester City at the Emirates on Saturday.
Tottenham's dream double has put them in pole position for fourth place but the odds of them making it three memorable, and hugely important wins in a row and knocking United off course, are long.
They have not beaten them for nine years and have to go back to 1989 for their last success at Old Trafford.
Their last two performances, however, have quickly erased the disappointment of their FA Cup semi-final defeat by Portsmouth.
"If we are not afraid we can win at United," said striker Roman Pavlyuchenko.
"They are a superbly-tuned machine but on our current form we should not be frightened. We have a difficult finish to the season, with two journeys to Manchester. We have a depressing recent run of results at Old Trafford and we need to correct it.
"I'm sure the Manchester City game (on May 5) will prove decisive in determining who gets fourth."
United, who would have hoped to have been in Champions League action this week but will instead turn up for Saturday's game on the back of a rare full week's rest at this stage of the season, know that this game represents their toughest remaining hurdle as they seek an unprecedented fourth successive title and a record 19th in all.
Chelsea, who have a three-better goal difference than United, must have thought the title was coming their way before last Saturday's double setback of their defeat by Spurs and Paul Scholes's stoppage time winner for United at Eastlands.
"What happened on Saturday was disappointing, especially with Manchester United's result," said midfielder Frank Lampard.
"When they scored in the last minute it was hard. If they had drawn the game it would have left us in a very healthy position but now it's tighter."
Chelsea will be without captain John Terry, suspended after his red card against Spurs, and midfielder John Obi Mikel, who has ankle ligament damage.
Didier Drogba continues to struggle with a groin problem that is likely to require surgery and Ancelotti might opt to use Nicolas Anelka as a sole striker giving Drogba time to recover ready to face Liverpool in better shape.
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